Also lots of liquidity in ETFs and other derivative products is provided based on being able to hedge quickly in other tickers with high probability. If I'm making a market in XLF (S&P Financials ETF), but my orders to hedge in BAC, GS, MS, C, ... all get held up in a batch auction, that's extra risk. I can't make a tight spread, large size market in the ETF since the price of the basket components can drift away after I get a fill.
Budish also argues that arbitrages aren't competed away. It's true that arbitrageurs will never eliminate arbitrages, only make them last for shorter periods of time. However, natural market participants can change their behavior to eliminate them, and they have.
If everyone trading S&P 500 futures also traded SPY with orders that arrived simultaneously, fewer arbitrages would exist to be exploited. You don't even need to be fast to do this, just precise with timing. This kind of routing is very common in equities markets and it's a big part of why many early HFT scalping models no longer work regardless of how fast you are.